Perfect-conductor sphere dipole interference (${\sigma }_{\mathrm{back}}=9\pi k^4{a}^6$)

An electrically small perfect conductor sphere has both an induced electric dipole moment and magnetic dipole moment. The latter contributes half the electric scattering amplitude in magnitude. The two amplitudes add in the backward direction and partially cancel in the forward direction. Thus the backward intensity is $9/4$ of the electric-only value and its radar cross section is $9\pi k^4{a}^6$. The correction persists at leading order as $ka\to 0$; discarding the magnetic term is a separate response approximation.^[ref]